Bharath-Shumway Naive Distance-to-Default

Install and import#

npm install fintech-algorithms

import { bharathShumwayNaiveDistanceToDefault } from "fintech-algorithms/credit-risk-and-default/probability-of-default/bharath-shumway-naive-distance-to-default";

Signature#

bharathShumwayNaiveDistanceToDefault(equity_value, debt_face_value, equity_volatility, prior_year_equity_return, horizon_years)

Computes the Bharath and Shumway naive distance to default, which approximates the Merton solve with closed-form substitutes for firm value and asset volatility instead of iterating.

Parameters#

Returns#

{ naive_firm_value: number; naive_debt_volatility: number; naive_asset_volatility: number; naive_distance_to_default: number; naive_default_probability: number; state: string; reason: string }

naive_firm_value is equity plus debt, naive_debt_volatility is the 0.05-plus-quarter-of-equity-volatility proxy, and naive_asset_volatility is the value-weighted blend of the two. naive_distance_to_default follows the Merton expression with those substitutes, and naive_default_probability is the normal tail beyond it. state is calculated.

Errors#

• When any argument is not a finite number — throws Error
• When equity_value, debt_face_value, equity_volatility, or horizon_years is not positive — throws Error

Complexity: time O(1), space O(1).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

120

80

0.35

0.08

1

Call#

bharathShumwayNaiveDistanceToDefault(equity_value, debt_face_value, equity_volatility, prior_year_equity_return, horizon_years)

Returns#

object with 7 fields: naive_firm_value, naive_debt_volatility, naive_asset_volatility, naive_distance_to_default, naive_default_probability, state, reason

{
  "naive_firm_value": 200,
  "naive_debt_volatility": 0.1375,
  "naive_asset_volatility": 0.265,
  "naive_distance_to_default": 3.62708766745,
  "naive_default_probability": 0.000143317997,
  "state": "calculated",
  "reason": "bharath-shumway-naive-approximation"
}

Other exports#

This module also exports logisticPdModel, probitPdModel, throughTheCyclePd, pointInTimePd, mertonDistanceToDefault, campbellHilscherSzilagyiDistressProbability, calculate. Every module additionally exports run as an alias of its primary function, and a meta object carrying its catalog id, domain, family, shape and article URL.

Diagrams#

Calculation flow#

flowchart LR
    S1["Validate equity debt volatility priorreturn window hor"]
    S2["Set nave firm value to equity plus debt"]
    S3["Calculate nave debt and asset volatility"]
    S4["Insert prioryear equity return as the papers drift pro"]
    S5["Calculate nave DD and PhiDD returning every component"]
    S1 --> S2
    S2 --> S3
    S3 --> S4
    S4 --> S5
    S5 --> D{"positive E F sigmaE and T with a causal priorreturn window"}
    D --> O["naive_distance_to_default + diagnostics"]
    O --> A["Audit: naivefirmvalue equals equityvalue plus debtfacevalue"]

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

• Forecasting Default with the Merton Distance to Default Model — Sreedhar T. Bharath and Tyler Shumway
• On the Pricing of Corporate Debt: The Risk Structure of Interest Rates — Robert C. Merton
• Supervisory Guidance on Model Risk Management — OCC, Board of Governors of the Federal Reserve System, and FDIC
• Evidence boundary

The rest of the Probability of Default family#

• Logistic PD ModelApplies a logistic link to a supplied linear credit score and reports the resulting default probability alongside the per-featu…
• Probit PD ModelApplies the standard normal cumulative distribution to a supplied linear latent score and reports the resulting default probabi…
• Through-the-Cycle PDTurns a multi-year history of obligor counts and default counts into annual default rates, averages them into a through-the-cyc…
• Point-in-Time PDOverlays a borrower-specific shift and a macro shift on the log-odds of a through-the-cycle default probability, returning the …
• Merton Distance-to-DefaultSolves the two-equation Merton system iteratively for the unobserved asset value and asset volatility implied by observed equit…
• Campbell-Hilscher-Szilagyi Distress ProbabilityEvaluates the published Campbell, Hilscher and Szilagyi twelve-month-lag logit with its eight accounting and market inputs, ret…